Analytic Löwdin alpha-function method for two-center electron-repulsion integrals over slater-type orbitals

Using the Löwdin alpha‐function method in which displaced orbitals are expanded in spherical harmonics, two‐center, two‐electron repulsion integrals of the Coulomb, hybrid, and exchange type are done analytically using Slater‐type orbitals. Computer algebra and integer arithmetic are used to obtain analytic results and avoid cancellation errors by the generation of rational matrix elements for C, E, and F matrices that are used to express the α‐function. The formula for the exchange integral is kept simple by reversing the order of integration over each part of a split quadrant. Only two basic integrals are used that are first efficiently evaluated by using look‐up tables and then used repeatedly.